For cases where we only study the gravitational forces, solving the Kepler’s equation is enough to propagate the orbit forward in time. However, when we want to take perturbations that deviate from Keplerian forces into account, we need a more complex method to solve our initial value problem: one of them is Cowell’s formulation.

In this formulation we write the two body differential equation separating the Keplerian and the perturbation accelerations:

For an in-depth exploration of this topic, still to be integrated in poliastro, check out this Master thesis

An earlier version of this notebook allowed for more flexibility and interactivity, but was considerably more complex. Future versions of poliastro and plotly might bring back part of that functionality, depending on user feedback. You can still download the older version here.

This means we successfully validated the model against an extremely simple orbit transfer with approximate analytical solution. Notice that the final eccentricity, as originally noticed by Edelbaum, is nonzero: